A pocket-spring core mattress of the type described in the introduction is known from European Preliminary Publication 154,076. Here too, bands or rows of closed pockets are formed, a helical spring being accommodated in each pocket. The bands or rows are connected to one another transversely relative to the direction of the band or of the row by coating an adhesive onto a tangential line of the pocket or onto the tangential lines of the pockets in one row and by pressing on the pockets of the adjacent row along the contact line or contact lines. A field arrangement of the individual pockets is thus possible, that is to say an arrangement in which the axes of the interconnected pockets or helical springs are arranged respectively at right angles to one another. The coating of the adhesive can be carried out in individual strips or in individual spots and connects the material of the pockets together directly transversely relative to the direction of the bands. For this purpose, the pockets of adjacent rows have to be pressed onto one another, and a certain setting time is necessary for the adhesive bond to harden. However, the arrangement of the adhesive coating is restricted to only a relatively small linear region when, for example, two rows of pockets with encased cylindrical springs are held pressed onto one another. This region becomes even shorter in terms of height when barrel springs are used. This results in a reduced retention of the springs relative to one another and a comparatively low dimensional accuracy of the mattress as a whole. Moreover, there is a problem in pressing on the adhesive coated on the pockets, because the material of the pockets sags or can experience a bulging deformation at the turns of the helical spring between the supporting points.